Some remarks on representations of Yang-Mills algebras
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ??(n) on n generators, for n ? 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-...
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00222488_v56_n1_p_Herscovich |
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| Sumario: | In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ??(n) on n generators, for n ? 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of ??(n) for n ? 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ? 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from ??(3) to ??(2, k) has in fact solvable image. © 2015 AIP Publishing LLC. |
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